Solving Absolute Value Equations

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve the equation |x| = a?

Back

To solve |x| = a, you set up two equations: x = a and x = -a.

Front

What does it mean if an absolute value equation has no solution?

Back

An absolute value equation has no solution if the expression inside the absolute value cannot equal the given value, such as |x| = -5.

Front

Solve for x: |x - 3| = 7.

Back

x = 10 or x = -4.

Front

What is the first step in solving |2x - 4| = 8?

Back

Set up two equations: 2x - 4 = 8 and 2x - 4 = -8.

Front

Solve for n: |-2 - 4n| = 34.

Back

n = -9 or n = 8.

Front

What is the solution to |6 - 2k| = 18?

Back

k = -6 or k = 12.

Front

Can the equation |6 - 2f| = -5 have a solution?

Back

No, because absolute values cannot be negative.

Front

Solve for a: |2a - 10| = 6.

Back

a = 8 or a = 2.

Front

What is the general form of an absolute value equation?

Back

The general form is |ax + b| = c, where a, b, and c are constants.